I've never done an aircraft carrier stability study, but I'm pretty sure stability calculations are done the same that for any other vessels. What is needed to know are the criteria to be met. Probably a relatively low GM, thus giving a high enough period of rolling to provide a good "platform stability", I presume.

What's the weather in Sing, Nice place I spent some time following the transformation of one ship for my company and we have till one in Jurong nearly finish. So to reply to your question , I work since long time now on big ship and i think that you have confused stability and seakeeping.
Stability is a part of seakeeping if i understand well you want to have a stable platform. As you know roll, pitch ... is not only link to the GM but to the inertia of your weight repartition so firstly, in order to have a good platform you have to take care of the weight and the location of the biggest. secondly the GM is a mix between form and weight so the form have a big part of the seakeeping (form of frame and fore and aft balanced form). When these two parameters are good is easy to add some external help :bilge keel, Stabilizator,rolling and pitching tank ....and for aircraft carrier moving mass under the landing deck. This technic is really efficiency. After all above job you must have a good software or the best is to work with a towing tank, there is some famous in Europe with big feedback, In Netherlands or denmark for exemple. I forgot something the speed it's very important because a stabilization at zero speed is not the same than at 20 or 30 Kts and the last things the weather and wave limit. If it's possible tell me more on your project (private message if you want), today I work on a new project for my company around 250/260 m and Singapore is one option for building this ship (if we have good price).

I hope that my reply help you, it's not a method but some way to take.

U.S. Navy aircraft carriers do not have gyro stabilizers, flume tanks, or active stabilizer fins to enhance their stability. They, like all of the other USN ships I am familiar with, do have bilge keels. Their primary weapon against excess rolling is their sheer size. If something is big enough, it can deal with nearly any wave that comes along. Not every wave, but most of them. Their secondary weapon against excess rolling is the weather routing messages they get while underway. If you aren't where the waves are, you won't respond to them.

I would not presume to tell a fisherman how to run his deck, but a supertanker is just a big gas can and I don't see any compelling need for the large superstructure at the stern.

The Japanese carrier captains were able to guide their ships well enough with out a superstructure. Yes, they later added them, but for a 'part time' carrier, and with todays closed circuit TV, I would stick to a completely flat deck for the sake of the planes.

Maybe a bridge that could be raised on a mast when making port, with the mast simply lowing into the hull for air ops.

Just install a modular deck over the existing plumbing you see on a tanker's deck.

If figure tankers are pretty cheap and they are just lots of steel plates.

If I was planning any carrier ops the first thing I would want is a couple big cheap super-tanker 'flat-tops' for several reasons.

While the operational robustness is impressive, a carrier is always one bad landing away from a USS Forestall disaster, I'd want a backup landing deck in the vicinity.

Rather not risk a bad landing, and thus the carrier, and ejecting from a questionable plane, you could have a extra, dedicated landing deck that could not only handle the risk, but could be configured in ways not practical on a carrier deck, such as a thick layer of foam, or yet to be invented apparatus such a massive net.

All ships of valuable to anti-ship missiles, I'd rather send a big hollow supertanker with a few planes on deck in harms way than a multi-billion dollar carrier with thousands of crew. An empty supertanker could take numerous massive hits with little effect, even more if the tanks were a little more compartmentalized than normal...just a few more flat steel plates.

When serving as a supertanker the crew might miss their nice views from the superstructure, but they might enjoy the benefits of land based fixed wing aircraft visiting.

Not sure how big or what type of aircraft could land on a supertanker without all sorts of modifications.

Not sure how much "hard to relocate" heavy equipment is currently housed in the superstructure.

Who wants to draft up an "artist's conception" to sell this to some status hungry oil sheik?

1938 - Frederick G. Creed, a Canadian, presents his idea for a small-waterplane-area twin-hull aircraft carrier to the British Admiralty.
Several years later Creed is permitted to show it to the U.S. Navy, but they do not pursue the concept.
1972 - Construction begins on the 190-ton SWATH workboat SSP KAIMALINO for NUC after 18 months of research by engineers at NUC
and nearly 2.5 years of design and confirmatory model testing4. Launching occurs in March, 1973.

Sq. Diddly: maybe the superstructure of a supertanker allows the crew to get away from the smell.

I like the idea of a family-sized economy backup carrier, but all you have to do to upscrew a carrier is make a hole in the deck, or deposit an incendiary device. So you install extra equipment and crew to deal with those eventualities. Then you install guns and other defensive stuff to protect the larger crew, since they may take it as a slight on their value to the nation if you don't. You don't want to spend all that money one a one-landing vessel so you put in elevators and hangars, and of course the pilot may have just been out of gas so you install refill capability and it wouldn't be fair to send the poor guy back up without ammo, oh, and if you're gonna send him back up you'll be wanting steam catapults ... Before you know it, you're well on the way to a proper carrier.

where
C = roll constant typically between 0.69 and 0.89 sec m for large ships
B = maximum beam at or below the water line, and
GM = maximum metacentric height.
The exact nature of C is based on experimental results from similar ships.

These periods denote the natural or ‘resonance’ periods of the ship. The actual periods of roll and/or pitch may depart from these depending on the forcing function of the waves, noting that the frequency of the wave encounter is heavily influenced by the forward motion of the ship.

Typical roll angles may be single digit degrees in sea-state 4, to several tens of degrees in sea-state 8. US Navy design limits are 45 deg. for most surface
ships, and 30 deg. for aircraft carriers.

The maximum pitch angle depends on sea-state and the ships length between
perpendiculars. A longer ship allows less pitch angle. Typical pitch angles may be 1 deg. to 2 deg. in sea-state 4, and perhaps 5 deg. to 11 deg. in sea-state 8. US Navy design limits are 10 deg. for most surface ships.

It seems like you could design an aircraft carrier with a VERY narrow BWL, and a submarine-like structure underwater (by enough to avoid making surface wake).

This way, you could dramatically minimize the rise/fall of the deck due to head-on waves, or waves coming from directly behind (kinda like exaggerating what they're already doing with the bulbous stern). Other than that though, I'm not the resource to be tapping to minimize roll from getting hit port or starboard by waves...we'll leave that to other designers